Activity coefficients symmetrical solutions

For such components, as the composition of the solution approaches that of the pure liquid, the fugacity becomes equal to the mole fraction multiplied by the standard-state fugacity. In this case,the standard-state fugacity for component i is the fugacity of pure liquid i at system temperature T. In many cases all the components in a liquid mixture are condensable and Equation (13) is therefore used for all components in this case, since all components are treated alike, the normalization of activity coefficients is said to follow the symmetric convention. ... 

The standard-state fugacity of any component must be evaluated at the same temperature as that of the solution, regardless of whether the symmetric or unsymmetric convention is used for activity-coefficient normalization. But what about the pressure At low pressures, the effect of pressure on the thermodynamic properties of condensed phases is negligible and under such con-... 

For symmetric electrolytes i=l for 1 2 electrolytes (e.g., Na2S04), 1 3 electrolytes (AICI3), and 2 3 electrolytes ([Al2(S04)3], the corresponding valnes of A, are 1.587, 2.280, and 2.551. Mean ionic activity coefficients of many salts, acids, and bases in binary aqneons solutions are reported for wide concentration ranges in special handbooks. 

As already mentioned, in solutions that are not symmetric mixtures it is conventional to treat the solute B (or solutes B, C,...) differently from the treatment accorded to the solvent A. The activity coefficient is still defined as the ratio Ub/xb, but the hmit at which it equals unity is taken as the infinite dilute solution of B in A ... 

In this section we shall always define the activity coefficients with respect to the symmetrical reference system. Comparing Eq. 8.7 and Eq. 8.17, we define the excess free enthalpy (excess Gibbs energy) gE per mole of a non-ideal binary solution as Eq. 8.18 ... 

This excess enthalpy hE corresponds to the heat of mixing of the non-ideal binary solution at constant pressure. Namely, hE = xf + x2h with - ht -h - -RT2(dlny JdT), where hf is the partial molar heat of mixing of substance i, ht is the partial molar enthalpy of i in the non-ideal binary solution, and h° is the molar enthalpy of pure substance i. Remind ourselves that the reference system for the activity coefficients is symmetrical. 

The rational activity coefficients cannot be evaluated in any simple manner. Following the model of Truesdell and Christ (16), a regular solution approach to the problem can lead to expressions for the rational activity coefficients. If the exchange sites have the same charge and approximately the same size, then a symmetrical solid solution will be formed where the rational activity coefficients for the two components are given by ... 

A similar expression can be obtained for the symmetric and the unsymmetric mole fraction activity coefficient. In a completely dissociated solution of n mol Na2S04, the mean molal activity coefficient is... 

In this chapter some aspects of the present state of the concept of ion association in the theory of electrolyte solutions will be reviewed. For simplification our consideration will be restricted to a symmetrical electrolyte. It will be demonstrated that the concept of ion association is useful not only to describe such properties as osmotic and activity coefficients, electroconductivity and dielectric constant of nonaqueous electrolyte solutions, which traditionally are explained using the ion association ideas, but also for the treatment of electrolyte contributions to the intramolecular electron transfer in weakly polar solvents [21, 22] and for the interpretation of specific anomalous properties of electrical double layer in low temperature region [23, 24], The majority of these properties can be described within the McMillan-Mayer or ion approach when the solvent is considered as a dielectric continuum and only ions are treated explicitly. However, the description of dielectric properties also requires the solvent molecules being explicitly taken into account which can be done at the Born-Oppenheimer or ion-molecular approach. This approach also leads to the correct description of different solvation effects. We should also note that effects of ion association require a different treatment of the thermodynamic and electrical properties. For the thermodynamic properties such as the osmotic and activity coefficients or the adsorption coefficient of electrical double layer, the ion pairs give a direct contribution and these properties are described correctly in the framework of AMSA theory. Since the ion pairs have no free electric charges, they give polarization effects only for such electrical properties as electroconductivity, dielectric constant or capacitance of electrical double layer. Hence, to describe the electrical properties, it is more convenient to modify MSA-MAL approach by including the ion pairs as new polar entities. 

Because the activities of species in the exchanger phase are not well defined in equation 2, a simplified model—that of an ideal mixture—is usually employed to calculate these activities according to the approach introduced bv Vanselow (20). Because of the approximate nature of this assumption and the fact that the mechanisms involved in ion exchange are influenced by factors (such as specific sorption) not represented by an ideal mixture, ion-exchange constants are strongly dependent on solution- and solid-phase characteristics. Thus, they are actually conditional equilibrium constants, more commonly referred to as selectivity coefficients. Both mole and equivalent fractions of cations have been used to represent the activities of species in the exchanger phase. Townsend (21) demonstrated that both the mole and equivalent fraction conventions are thermodynamically valid and that their use leads to solid-phase activity coefficients that differ but are entirely symmetrical and complementary. 

Definition of single ion activity coefficient. For simplicity, only solutions of symmetrical binary univalent electrolytes will be considered here. 

What are the equations for computing the Gibbs free energy, enthalpy, and entropy of formation of a binary symmetrical regular solution How are the rational activity coefficients (/I values for the solid components) related to their mole fractions in such a solid solution ... 

An example of the use of this method is given in Figure 3.5.7 for the methyl acetate(l) and cydohexane(2) binary system (Pividal et al. 1992) at 313 K. The infinite dilution activity coefficient of each component in the other is available for this binary pair, the mixture is nearly symmetric and deviates only moderately from ideal solution behavior = 4.81/4.54). The solutions of eqns. (3.5.9 to 3.5.11)... 

The second source of data available for multicomponent mixtures are the excess thermodynamic quantities. These are equivalent to activity coefficients that measure deviations from symmetrical ideal solutions and should be distinguished carefully from activity coefficients which measure deviations from ideal dilute solutions (see chapter 6). In a symmetrical ideal (SI) solution, the... 

A choice must be made for the reference state for the solute either the pure liquid (possibly supercooled), or the solute at infinite dilution in the solvent. The latter differs from the conventional solute standard state only in the use of the mole fraction scale rather than molality units. The activity coefficient of a symmetrical salt MX is either... 

If above relatiOTi can not be determined, it is sometimes possible to deduce activity coefficient values for components in solid phase based on thermodynamic solid solutimi model. For example, if symmetrical solvus (Fig. 1.2) exists for a binary system, regular solution model could be applicable to the estimation of activity coefficients and other thermodynamic parameters values of solid solution... 

We see that for the symmetrical equation (and most other useful activity coefficient equations) the activity coefficient of the solute is proportional to the square of the concentration of the solvent. For most gases dissolved in liquids, the change in solute concentrations is so small that the concentration of the solvent is practically constant, 1.00. Thus, over the range of practical interest the activity coefficient— Raoult s law type—of the dissolved solute gas is practically constant, which is the same as saying that Henry s law is obeyed within experimental accuracy, with. extrapolated iT-... 

Lindenbaum S, Boyd GE. (1964) Osmotic and activity coefficients for the symmetrical tetraalkyl ammonium halides in aqueous solution at 25°C. J Phys Chem 68 911-917. 

This picture suggests that the more size-symmetric ion pairs such as KCl or NaCl should exhibit stronger attraction in solution than the size-asymmetric salt LiCl. This local argument should also have a bearing on integral thermodynamic properties such as osmotic coefficients, activity coefficients, maximal solubilities or heats of solution (compare Fig. 1). Most of these properties are difficult to obtain from simulations. The osmotic coefficient (p is comparably straightforward to calculate. It is related to the osmotic pressure O via... 

Equation (E7.9F) shows that if the polarizabilities are equal, we have an ideal solution in all other cases A > 0 (for spherically symmetric nonpolar molecules) Thus, we are much more likely to find in nature a case where like interactions dominate (i.e., have lower energy) and the activity coefficients (based on the Lewis/RandaU reference state) are greater than 1 for example, see Equations (7.55) and (7.56). 

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